We take a=x,b=2y, c=3z in the expansion ( a+b+c ) #160;^ 2 = a ^ 2 + b ^ 2 + c ^ 2 +2ab+2bc+2ca We obtain ( x+2y+3z ) #160;^ 2 = x ^ 2 + (2y ...

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Algebraic Identities

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Question

Expand: ${(x + 2 y + 3 z)}^{2}$

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Solution

We take $a = x, b = 2 y, c = 3 z$ in the expansion
${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
We obtain
${(x + 2 y + 3 z)}^{2} = x^{2} + {(2 y)}^{2} + {(3 z)}^{2} + 2 x (2 y) + 2 (2 y) (3 z) + 2 (3 z) x = x^{2} + 4 y^{2} + 9 z^{2} + 4 x y + 12 y z + 6 z x$

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